Subfamilies of bi-univalent functions governed by Bernoulli polynomials

Volume 40, Issue 3, pp 341--352 https://dx.doi.org/10.22436/jmcs.040.03.04

Publication Date: July 08, 2025 Submission Date: March 03, 2025 Revision Date: May 15, 2025 Accteptance Date: June 12, 2025

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Authors

S. R. Swamy - Department of Information Science and Engineering, Acharya Institute of Technology, Bengaluru-560 107, Karnataka, India. B. A. Frasin - Faculty of Science, Department of Mathematics, Al al-Bayt University, Mafraq, Jordan. K. Venugopa - Department of Information Science and Engineering, Acharya Institute of Technology, Bengaluru-560 107, Karnataka, India. T. M. Seoudy - Department of Mathematics, Jamoum University College, Umm Al-Qura University, Makkah, Saudi Arabia.

Abstract

In the context of univalent function theory, special functions play an important role and have been studied by a number of researchers earlier. This article presents and examines two subfamilies of bi-univalent functions that are governed by Bernoulli polynomials in the open unit disk. We obtain limits on initial coefficients for functions in the specified subfamilies. The Fekete-Szegő problem is also addressed for the elements of the subfamilies that have been defined. We also present some new results and discuss pertinent links to earlier findings.

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Keywords

• Regular functions
• subordination
• bi-univalent functions
• Bernoulli polynomials

MSC

•  30C45
•  05A15
•  11B39

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